Question

A CD is spinning on a CD player. In 12 radians, the cd has reached an angular speed of 17 r a d s by accelerating with a constant acceleration of 3 r a d s 2 . What was the initial angular speed of the CD

Answer 1

The initial angular speed of the CD is equal to 14.73 rad/s.

Step-by-step explanation:

Given that,

Angular displacement,
`\theta=12\ rad`

Final angular speed,
`\omega_f=17\ rad/s`

The acceleration of the CD,
`\alpha =3\ rad/s^2`

We need to find the initial angular speed of the CD. Using third equation of kinematics to find it such that,

`\omega_f^2=\omega_i^2+2\alpha \theta\\\\\omega_i^2=\omega_f^2-2\alpha \theta`

Put all the values,

`\omega_i^2=(17)^2-2* 3* 12\\\\\omega_i=√(217)\\\\\omega_i=14.73\ rad/s`

So, the initial angular speed of the CD is equal to 14.73 rad/s.